Convexity of the Proximal Average

Jennifer A. Johnstone, Valentin R. Koch and Yves Lucet ()
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Jennifer A. Johnstone: University of British Columbia Okanagan
Valentin R. Koch: University of British Columbia Okanagan
Yves Lucet: University of British Columbia Okanagan

Journal of Optimization Theory and Applications, 2011, vol. 148, issue 1, No 7, 107-124

Abstract: Abstract We complete the study of the convexity of the proximal average by proving it is convex as a function of each of its parameters separately, but not jointly convex as a function of any two of its parameters. We present an interpolation-based plotting algorithm that takes advantage of the partial convexity of the proximal average, and improves the plotting time by a factor of 100, while reducing picture sizes by a factor of 10.

Keywords: Convex analysis; Proximal average; Convexity; Interpolation (search for similar items in EconPapers)
Date: 2011
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DOI: 10.1007/s10957-010-9747-5

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